论文标题
关于符号差异的伴随作用
On the adjoint action of the group of symplectic diffeomorphisms
论文作者
论文摘要
我们研究紧凑型象征性歧管（$ x，ω$）对$ c^\ infty（x）$和函数$ c^\ infty（x）\ to \ mathbb r $的动作。我们描述了$ c^\ infty（x）$上不变凸功能的各种属性。除其他方面，我们表明，连续的凸功能$ c^\ infty（x）\ to \ mathbb r $在该动作下是不变的，在所谓的严格重排下会自动不变，并且它们在$ c^\ infty（x）$的SUP Norm topology中是连续的；但这通常是不正确的，如果降低了凸状条件。
We study the action of Hamiltonian diffeomorphisms of a compact symplectic manifold ($X,ω$) on $C^\infty(X)$ and on functions $C^\infty(X)\to \mathbb R$. We describe various properties of invariant convex functions on $C^\infty(X)$. Among other things we show that continuous convex functions $C^\infty(X)\to \mathbb R$ that are invariant under the action are automatically invariant under so called strict rearrangements and they are continuous in the sup norm topology of $C^\infty(X)$; but this is not generally true if the convexity condition is dropped.
